ABSTRACT
When a relation 0 is a congruence relation on an algebra A of type T, we can form the quotient algebra A/0. The Homomorphic Image Theorem tells us that any homomorphic image of an algebra A is isomorphic to such a quotient algebra of A. Another important use of the quotient algebra was seen in Section 6.4: taking A to be the absolutely free algebra T,-(X) of type T and 0 to be the set IdK of identities of a class K of algebras of type T, we formed the quotient algebra .F.,-(X)1IdK, called the relatively free algebra with respect to K over the set X.
